The polynomial generated from the given zeros is: $ P(x) = x^4-2x^3-71x^2+72x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 9 $ | $ x-9 $ |
$ 1 $ | $ x-1 $ |
$ 0 $ | $ x $ |
$ -8 $ | $ x+8 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-9 \right) \cdot \left( x-1 \right) \cdot x \cdot \left( x+8 \right) = x^4-2x^3-71x^2+72x $$